And, like, idk, man. 130 is pretty smart but not “famous for their public intellectual output” level smart.
Yeah “2 sds just isn’t that big a deal” seems like an obvious hypothesis here (“People might over-estimate how smart they are” is, of course, another likely hypothesis).
Also of course OP was being overly generous by assuming that it’s a normal distribution centered around 128. If you take a bunch of random samples of a normal distribution, and only look at subsamples with median 2 sds out, in approximately ~0 subsamples will you find it equally likely to see + 0 sds and +4 sds.
If you take a bunch of random samples of a normal distribution, and only look at subsamples with median 2 sds out, in approximately ~0 subsamples will you find it equally likely to see + 0 sds and +4 sds.
Wait, are you claiming +0 SD is significantly more likely than +4 SD in a subsample with median +2 SD, or are you claiming that +4 SD is more likely than +0 SD? And what makes you think so?
The former. I think it should be fairly intuitive if you think about the shape of the distribution you’re drawing from. Here’s the code, courtesy of Claude 3.5. [edit: deleted the quote block with the code because of aesthetics, link should still work].
Yeah “2 sds just isn’t that big a deal” seems like an obvious hypothesis here (“People might over-estimate how smart they are” is, of course, another likely hypothesis).
Also of course OP was being overly generous by assuming that it’s a normal distribution centered around 128. If you take a bunch of random samples of a normal distribution, and only look at subsamples with median 2 sds out, in approximately ~0 subsamples will you find it equally likely to see + 0 sds and +4 sds.
Wait, are you claiming +0 SD is significantly more likely than +4 SD in a subsample with median +2 SD, or are you claiming that +4 SD is more likely than +0 SD? And what makes you think so?
The former. I think it should be fairly intuitive if you think about the shape of the distribution you’re drawing from. Here’s the code, courtesy of Claude 3.5. [edit: deleted the quote block with the code because of aesthetics, link should still work].